Chain tensor products and interval effect algebras
An effect algebra is an algebra \(P= (P,\oplus,0,1)\), where \(\oplus\) is a partial binary operation which is commutative and associative, given \(a\in P\) there is a unique element \(a'\) in \(P\) such that \(a \oplus a'= 1, \) and if \( a \oplus 1\) is defined, then \(a= 0.\) The tensor product of D-posets (an equivalent structure) has been introduced by the reviewer [``Tensor product of difference posets'', Trans. Am. Math. Soc. 347, 1043-1057 (1995; Zbl 0859.03031)]. Nowadays it is known that there are stateless effect algebras for which there is no tensor product [\textit{S. Gudder} and \textit{R. Greechie}, ``Effect algebra counterexamples'', Math. Slovaca 46, 317-325 (1996)]. The author of the present article introduces a chain tensor product and normal interval effect algebras (including, e.g., Hilbert space effect algebras), and he studies relations among them.
scientific article; zbMATH DE number 1066037
scientific article